APPENDIX D
Equations and assumptions adopted in railway noise
calculation :
- Airborne noise speed correction Dva : 30log(v/vo)
(Equation 1)
- Structure-radiated noise speed correction Dvs : 25log(v/vo)
(Equation 2)
- Attenuation due to geometric spreading Ds:
(Equation
3)
- Angle of view correction Dq: 10log(q/180)
(Equation 4)
- The barrier attenuation for condition where adequate sound absorption is placed on the source side was calculated using the following equation for point sources :
(Equation
5)
where N, the Fresnel number, is a function of the path length difference.
The attenuation of sound from a line source parallel to the edge of the barrier is calculated by integration over the segment angle. The numerical integration for line source correction is carried out in the modelling process.
- Conversion of the Maximum Sound Pressure Level, Lmax, to the Equivalent Noise Level, Leq :
(Equation 6)
where R = number of trains per hour ;
d = distance of the receiver from the track centerline (m) ;
l = length of the train (m) ;
v = speed of the train (km/h) ;
q = the angle of view of the railway segment ;
do = reference distance = 25m ;
vo = reference train speed = 100km/h .
- Correction for façade effect = 2.5dB(A)
- Corrections for Points and Crossings :
|
Track Conditions |
At-grade |
Viaduct |
|
Points and Crossings |
+7.0dB(A) |
+7dB(A) |
On viaduct and at-grade plenum, at crossovers where plenum cannot be provided, the source noise level is the noise source term + 7dB(A).
II. Sample
Rail Noise Calculation
To illustrate the calculation procedure adopted in the operational noise impact assessment, the unmitigated noise level prediction for Representative Noise Sensitive Receiver 13-2 is detailed as follows.
RNSR 13-2 is located at 15m from the centerline of the track segment and 10.8m below the top of rail. From the speed profile provided by KCRC, the average train speed determined for the segment is 86.3km/h.
- Positions of the receiver and the track segment with major noise contribution
|
|
Easting |
Northing |
Elevation (mPD) |
|
Up track segment #84 |
830057.6 |
840939.7 |
17.8 |
|
RNSR 13-2 |
830061.5 |
840926.5 |
7.1 |
In the rail noise prediction, the major noise components, namely airborne noise, structure-radiated noise and air-conditioner (A/C) noise, were modelled separately and combined to obtain the total noise.
a) Airborne Noise
- Airborne noise level at 25m from track centerline was calculated by applying the speed correction to the source noise level.
Source noise level (Airborne) for single plenum system = 75.3dB(A)
Lmax, A/B, 25m = 75.3 + 30log(86.3/100) = 73.4dB(A) (using Equation 1)
- Attenuation due to geometric spreading Ds:
Setback distance from plenum gap = 13.5 m
Vertical distance from plenum gap = 11.6 m
Slant distance from plenum gap = 17.9 m
The reference distance, do, is 25m and the length of a 12-car train, l, is 300m.
Ds = 1.5 dB(A) (using Equation 3)
- Angle of view correction Dq:
Segment angle of view = 65°
Dq = -4.4dB(A) (using Equation 4)
- Barrier attenuation :
The path length difference estimated for the 1.2m parapet wall on the standard viaduct structure is 1.6m.
The Reference Viaduct Noise Spectrum adopted in the West Rail EIA study was used in calculating the barrier attenuation
Point-source barrier attenuation Db = -20.9dB(A) (using Equation 5)
- Maximum airborne noise level at RNSR13-2 due to segment #84,
Lmax, A/B = Lmax, A/B, 25m + Dq + Ds + Db = 73.4 + 1.5 - 4.4 -20.9 = 49.5dB(A)
- Airborne noise contribution from segment #84 was obtained by converting Lmax to Leq and with façade effect correction applied:
For baseline condtions, the train frequency is taken as 12 trains per hour per direction.
Leq, A/B = 49.5 + 10log(12(1.5´17.9+300)/86.3) -30 + 2.5 = 38.6dB(A)
(using Equation 6)
b) Structure-radiated Noise
- Structure-radiated noise level at 25m from track centerline was calculated by applying the speed correction to the source noise level.
Source noise level (Structure-radiated) for Low Vibration Track = 66.5dB(A)
Lmax, S/R, 25m = 66.5 + 25log(86.3/100) = 64.9dB(A) (using Equation 2)
- Attenuation due to geometric spreading Ds:
Setback distance from viaduct structure = 15.0 m
Vertical distance from viaduct structure = 8.7 m
Slant distance from viaduct structure = 17.3 m
The reference distance, do, is 25m and the length of a 12-car train, l, is 300m.
Ds = 1.6 dB(A) (using Equation 3)
- Angle of view correction Dq:
Segment angle of view = 65°
Dq = -4.4dB(A) (using Equation 4)
- Maximum structure-radiated noise level at RNSR13-2 due to segment #84,
Lmax, S/R = Lmax, S/R, 25m + Dq + Ds = 64.9 + 1.6 - 4.4 = 62.1dB(A)
- Structure-radiated noise contribution from segment #84 was obtained by converting Lmax to Leq and with façade effect correction applied:
For baseline condtions, the train frequency is taken as 12 trains per hour per direction.
Leq, S/R = 62.1 + 10log(12(1.5´17.3+300)/86.3) -30 + 2.5 = 51.1dB(A)
(using Equation 6)
c) Air-Conditioner (A/C) Noise
- A/C noise level at 25m from track centerline for East Rail Refurbished Train :
Lmax, A/C, 25m = 62.8dB(A)
- Attenuation due to geometric spreading Ds:
Setback distance from plenum gap = 15.0 m
Vertical distance from plenum gap = 14.4 m
Slant distance from plenum gap = 20.8 m
The reference distance, do, is 25m and the length of a 12-car train, l, is 300m.
Ds = 0.8 dB(A) (using Equation 3)
- Angle of view correction Dq:
Segment angle of view = 65°
Dq = -4.4dB(A) (using Equation 4)
- Barrier attenuation :
The path length difference estimated for the 1.2m parapet wall on the standard viaduct structure is 0.3m.
The Reference Viaduct Noise Spectrum adopted in the West Rail EIA study was used in calculating the barrier attenuation
Point-source barrier attenuation Db = -16.8dB(A) (using Equation 5)
- Maximum A/C noise level at RNSR13-2 due to segment #84,
Lmax, A/C = Lmax, A/C, 25m + Dq + Ds + Db = 62.8 + 0.8 - 4.4 -16.8 = 42.4dB(A)
- A/C noise contribution from segment #84 was obtained by converting Lmax to Leq and with façade effect correction applied:
For baseline condtions, the train frequency is taken as 12 trains per hour per direction.
Leq, A/C = 42.4 + 10log(12(1.5´20.8+300)/86.3) -30 + 2.5 = 31.5dB(A)
(using Equation 6)
d) Total Noise
The total noise contribution from segment #84 was obtained by summing the noise contribution from the three wayside noise components.
- Maximum noise level at RNSR13-2 due to segment #84,
Lmax, total = log sum (Lmax, A/B , Lmax, S/R , Lmax, A/C) = 62.4dB(A)
- Total noise contribution from segment #84,
Leq, total = log sum (Leq, A/B , Leq, S/R , Leq, A/C) = 51.4dB(A)
Similarly, noise contribution from each segment of both Southbound and Northbound track of the Spur Line was calculated. For track segment where points and crossings are located, correction factors were applied to account for the augmentation of rolling noise levels occur when trains pass over these track segments.
The maximum noise level due to a train passby and the predicted noise level at the RNSR13-2 were obtained by summing the noise levels from all segments of both up and down track of the Spur Line. Prediction results, with breakdown of contribution from major noise components, are given in Appendix E.